The Bhoys went down 3-1 to the Norwegian side in Group A on Thursday evening.
Hosts Molde took the lead as early as the 11th minute when Ola Kamara steered the ball past goalkeeper Craig Gordon.
Vegard Forren doubled the home team’s advantage in the 18th minute, and although Kris Commons' superb finish halved the deficit in the 55th minute, Mohamed Elyounoussi immediately replied.
Former Celtic striker Hartson was following the match, and he was not impressed with the way the Hoops defended.
The former Wales international was also bemused to see attacking midfielder Commons taken off for forward Nadir Ciftci in the 76th minute.
Comical decision to bring Commons off with 20 mins to go. Let's not paper over the cracks.. Defensively Celtic over the place.— John Hartson (@JohnHartson10) October 22, 2015
Strange decision. @kcommons15 should never have been taken off. Johansen yes. Sad to hear fans boo-ing.— Frank McAvennie (@MaccaFrank) October 22, 2015
Celtic are at the foot of the Europa League Group A at the moment with just two points from three matches, two points behind second-place Fenerbahce.
The Bhoys are back in action on Sunday when they take on Dundee United at Celtic Park in the Scottish Premiership.